1. Evolving Factor Analysis The evolution of a chemical system is gradually known by recording a new response vector at each stage of the process under study. EFA performs subsequent PCA on gradually increasing submatrices in the process direction, enlarged by adding one new row at a time. This procedure is performed from top to bottom of the data set (forward EFA) and from bottom to top (backward EFA) to investigate the emergence and the decay of the process contribution, respectively. The forward and backward EFA plots are built by representating the singular values of each PCA analysis vs. the process variable related to the last row included in the window analyzd.

27. 1.4327 0.0024 Singular values (0-2 sec)

28. 2.2664 0.0083 0.0000 Singular values (0-4 sec)

29. 3.2730 0.0231 0.0000 0.0000 Singular values (0-6 sec)

30. 4.4044 0.0563 0.0001 0.0000 Singular values (0-8 sec)

31. 5.5834 0.1245 0.0004 0.0000 Singular values (0-10 sec)

32. 6.7299 0.2517 0.0012 0.0000 Singular values (0-12 sec)

33. 7.7864 0.4668 0.0036 0.0000 Singular values (0-14 sec)

34. 8.7323 0.7956 0.0099 0.0000 Singular values (0-16 sec)

35. 9.5808 1.2484 0.0244 0.0000 Singular values (0-18 sec)

36. 10.3637 1.8119 0.0552 0.0000 Singular values (0-20 sec)

37. 11.1136 2.4512 0.1133 0.0000 Singular values (0-22 sec)

38. 11.8506 3.1232 0.2110 0.0000 Singular values (0-24 sec)

39. 12.5772 3.7923 0.3561 0.0000 Singular values (0-26 sec)

40. 13.2808 4.4360 0.5455 0.0000 Singular values (0-28 sec)

41. 13.9413 5.0402 0.7623 0.0000 Singular values (0-30 sec)

42. 14.5360 5.5893 0.9812 0.0000 Singular values (0-32 sec)

43. 15.0430 6.0633 1.1776 0.0000 Singular values (0-34 sec)

44. 15.4449 6.4435 1.3359 0.0000 Singular values (0- 36 sec)

45. 15.7348 6.7216 1.4512 0.0000 Singular values (0- 38 sec)

46. 15.9215 6.9040 1.5268 0.0000 Singular values (0- 40 sec)

47. 16.0273 7.0098 1.5713 0.0000 Singular values (0- 42 sec)

48. 16.0794 7.0634 1.5942 0.0000 Singular values (0- 44 sec)

49. 16.1015 7.0868 1.6044 0.0000 Singular values (0- 46 sec)

50. 16.1096 7.0955 1.6083 0.0000 Singular values (0-48 sec)

51. 16.1122 7.0983 1.6096 0.0000 Singular values (0-50 sec)

52. 0.7231 0.0017 0.000 0.000 Singular values (50-48 sec)

53. 1.2648 0.0060 0.0000 0 Singular values (50-46 sec)

54. 2.0245 0.0164 0.0000 0.0000 Singular values (50-44 sec)

55. 3.0143 0.0395 0.0000 0.0000 Singular values (50-42 sec)

56. 4.2074 0.0865 0.0001 0.0000 Singular values (50-40 sec)

57. 5.5408 0.1738 0.0003 0.0000 Singular values (50-38 sec)

58. 6.9305 0.3215 0.0009 0.0000 Singular values (50-36 sec)

59. 8.2934 0.5483 0.0029 0.0000 Singular values (50-34 sec)

60. 9.5650 0.8639 0.0082 0.0000 Singular values (50-32 sec)

61. 10.7064 1.2627 0.0213 0.0000 Singular values (50-30 sec)

62. 11.7008 1.7245 0.0504 0.0000 Singular values (50-28 sec)

63. 12.5455 2.2228 0.1080 0.0000 Singular values (50-26 sec)

64. 13.2478 2.7381 0.2091 0.0000 Singular values (50-24 sec)

65. 13.8235 3.2656 0.3639 0.0000 Singular values (50-22 sec)

66. 14.2956 3.8130 0.5684 0.0000 Singular values (50-20 sec)

67. 14.6900 4.3880 0.8003 0.0000 Singular values (50-18 sec)

68. 15.0288 4.9811 1.0266 0.0000 Singular values (50-16 sec)

69. 15.3247 5.5579 1.2200 0.0000 Singular values (50-14 sec)

70. 15.5782 6.0693 1.3680 0.0000 Singular values (50-12 sec)

71. 15.7824 6.4753 1.4711 0.0000 Singular values (50-10 sec)

72. 15.9307 6.7613 1.5372 0.0000 Singular values (50-8 sec)

73. 16.0254 6.9387 1.5759 0.0000 Singular values (50-6 sec)

74. 16.0776 7.0349 1.5963 0.0000 Singular values (50- 4 sec)

75. 16.1022 7.0801 1.6058 0.0000 Singular values (50-2 sec)

76. 16.1122 7.0983 1.6096 0.0000 Singular values (50-0 sec)

78. Using MATLAB for evolving factor analysis

79. hplc.m file Creating HPLC-DAD data

80. HPLC-DAD data for three components system

82. EFA.m file Evolving Factor Analysis

83. Retention Time Wavelength D

85. Delete the SVF and SVB variables from the memory in work space

87. Creating the SVF matrix with (m  m- 1) dimensions and all elements equal to zero

88. An example for zeros command in MATLAB

101. Plot the results of forward analysis

113. Change in order of columns of the matrix

116. Comparison of real and estimated profiles

117. ? Employ the EFA in wavelength direction of data matrix and interpret the results

118. Transformation the concentration windows calculated with EFA to concentration profiles Retention Time

119. C= S T = Concentration matrix Score matrix Transformation matrix c 1 = S t 1 = Concentration vector Score matrix Transformation vector = c 0 = S 0 t 1 0= t 11 s 1 + t 21 s 2 + t 31 s 3

120. HPLC-DAD data for three components system

121. Results from EFA Retention Time From row number 35 to 61

122. concEFA.m file for calculation the concentration profiles according to results of EFA

126. Comparison the results with true values

127. ? Use the concEFA.m file and calculate the concentration profile for third component

128. Application of EFA in chemical equilibria study Stepwise dissociation of triprotic acid H 3 A

130. H3A.m file for simulating the spectrophotometric monitoring of pH-meteric titration

132. Evolving Factor Analysis (EFA)

134. ? Use the H3A.m file and investigate the effects of pKas on results of EFA.

135. Application of EFA in chemical Linetics study Consecutive reaction

137. consecutive.m file for simulating the spectrophotometric monitoring of consecutive A B C reaction

139. Evolving Factor Analysis (EFA)

141. ? Use the consecutive.m file and investigate the effects of rate constants on results of EFA.

142. Fixed concentration of interference and EFA

144. EFA

145. HPLC-DAD data after column mean centering

146. Results of forward and backward eigen analysis

147. Results of applying EFA on mean centered data

148. Score plot without mean centering

149. Score plot after mean centering

150. Distribution of objects of a two component system O A2 A1

151. Mean centering O A1 A2

152. Mean centering and then PCA O PC1 PC2

153. Distribution of objects of a two component system O A1 A2

154. Mean centering on window data O A1 A2

155. Before appearance the analyte the variance is equal to zero Mean centering on window data and then PCA O PC1 PC2

156. Before appearance the analyte the variance is equal to zero Mean centering on window data and then PCA O PC1 PC2

157. O PC1 PC2 Before appearance the analyte the variance is equal to zero Mean centering on window data and then PCA

158. Before appearance the analyte the variance is equal to zero Mean centering on window data and then PCA O PC1 PC2

159. Mean centering on window data O A1 A2

160. Mean centering and then PCA on window data O PC1 PC2

161. Mean centering on window data O A1 A2

162. Mean centering and then PCA on window data O PC1 PC2

163. Mean centering on window data O A1 A2

164. Mean centering and then PCA on window data O PC1 PC2

165. IEFA.m Evolving factor analysis in the presence of fixed concentration interferent

166. Results of applying IEFA.m file

168. Comparison between results of IEFA and real values of analyte

169. ? Use IEFA.m file and analyze the three co-eluting components system with fix concentration of one of them

170. Titration of H3A in the presence of an inert species

172. EFA results

173. EFA results in the absence of interference

174. ? WHY?